Yazar "Kilar, Neslihan" seçeneğine göre listele

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    A NEW CLASS OF GENERALIZED FUBINI POLYNOMIALS AND THEIR COMPUTATIONAL ALGORITHMS
    (Univ Belgrade, Fac Electrical Engineering, 2023) Kilar, Neslihan
    The aim of this paper is to give many new and elegant formulas for a new class of generalized Fubini polynomials with the aid of generating functions and their functional equations. By using these formulas, some computational algorithms involving a new class of generalized Fubini polynomials and special polynomials and numbers are constructed. Using these algorithms, some values of these numbers and polynomials are computed. Finally, some remarks and observations on the results of this paper are presented.
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    A Note on Two Parametric Kinds of Eulerian-type Polynomials Related to Some Special Numbers and Polynomials
    (American Institute of Physics Inc., 2023) Kilar, Neslihan; Simsek, Yilmaz
    The main idea of this paper is to give some identities and applications of the two parametric kinds of Eulerian-type polynomials. By using generating functions and functional equations of these special polynomials, we derive some identities and relations associated with the two parametric kinds of Eulerian-type polynomials, the Hermite polynomials, and well-known combinatorial numbers and polynomials. Moreover, we give a remark on these special polynomials and functions. © 2023 American Institute of Physics Inc.. All rights reserved.
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    ASYMPTOTIC EXPRESSIONS AND FORMULAS FOR FINITE SUMS OF POWERS OF BINOMIAL COEFFICIENTS INVOLVING SPECIAL NUMBERS AND POLYNOMIALS
    (Univ Prishtines, 2023) Kilar, Neslihan
    The main objective in this paper is to study on special numbers and polynomials that contain finite sums of powers of binomial coefficients. By using generating function methods, some formulas and relations related to these numbers and the Apostol-Bernoulli and Apostol-Euler numbers of nega-tive higher order, the Bernoulli and Euler numbers, the Stirling type numbers, the combinatorial numbers, the Bell polynomials, the Fubini type polynomials, and the Legendre polynomials are presented. Moreover, asymptotic expres-sions of the finite sums of powers of binomial coefficients for these numbers are given. Some numeric values of these asymptotic expressions are illustrated by the tables. Finally, some inequalities for these numbers are given.
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    Building generating functions for degenerate Simsek-type numbers and polynomials of higher order
    (MTJPAM Turkey, 2024) Kilar, Neslihan
    The objective of this paper is to build generating functions for new families of special numbers and polynomials, which are called higher order degenerate Peters-type Simsek numbers and polynomials of the second kind. Using generating function methods, we give both some fundamental properties of these functions with some relations among the higher order degenerate Peters-type Simsek numbers and polynomials of the second kind, the Stirling numbers of the first kind, the higher order degenerate Changhee numbers and polynomials, and the higher order Apostol-type Daehee numbers and polynomials. We also give some plots of these numbers and polynomials via Wolfram Cloud. Further, applying a partial derivative operator to these generating functions, we obtain derivative formulas for these new families. Eventually, we present further remarks on our new families including their generating functions. © 2024, MTJPAM Turkey. All rights reserved.
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    Combinatorial Sums and Identities associated with Functional Equations of Generating Functions for Fubini Type Polynomials
    (Gazi Univ, 2023) Kilar, Neslihan
    Using generating functions with their functional equations method, a great number of novel combinatorial sums, formulas, and recurrence relation including Fubini type polynomials and numbers, Stirling type numbers, and Apostol type polynomials are given. Applying Riemann integral to this generating function with their functional equations, some identities involving Cauchy and Stirling numbers are obtained. Moreover, some interpretations about the results are given.
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    Families of unified and modified presentation of Fubini numbers and polynomials
    (MTJPAM Turkey, 2023) Kilar, Neslihan; Simsek, Yilmaz
    The goal of this paper is to define new families of unified and modified presentation of the Fubini numbers and polynomials with their generating functions. Using generating functions and their functional equations, many properties of these polynomials and numbers are presented. Relations among unified and modified presentation of the Fubini numbers and polynomials, Stirling type numbers, combinatorial type polynomials, and unified presentation of the generalized Bernoulli, Euler and Genocchi polynomials are given. Many novel identities and relations including these polynomials and numbers are also given. Moreover, new Hurwitz-Lerch type zeta functions, which interpolate unified and modified presentation of the Fubini numbers and polynomials at negative integers, are defined. Furthermore, suitable links of identities and relations, which are found in this paper, with those in earlier and future studies are indicated. © 2023, MTJPAM Turkey. All rights reserved.
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    Formulae bringing to light from certain classes of numbers and polynomials
    (Springer-Verlag Italia Srl, 2023) Kilar, Neslihan; Kim, Daeyeoul; Simsek, Yilmaz
    With aid of generating functions and their functional equation methods and special functions involving trigonometric functions, the motivation of this paper is to study by blending certain families polynomials associated with the Bernoulli numbers and polynomials, the Euler numbers and polynomials, the Hermite type polynomials, the Stirling numbers, the telephone numbers, the Chebyshev polynomials. Therefore, the purpose of this paper is to examine certain families of numbers and functions related to generalized Hermite-Kampe de Feriet polynomials and trigonometric functions. By using functional equations of generating functions, we derive numerous new formulae and relations involving parametric Hermite type polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the generalized Hermite-Kampe de Feriet polynomials and the telephone numbers. Moreover, applying derivative operator to these generating functions, we give many recurrence relations and computational formulae, and certain finite sums. Finally, some special cases of these results are reduced to not only the well-known Chebyshev polynomials, which have applications in a wide variety of different areas, but also special trigonometric functions and finite sums.
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    Formulas for Fubini type numbers and polynomials of negative higher order
    (MTJPAM Turkey, 2023) Kilar, Neslihan
    The present paper deals with the Fubini type numbers and polynomials with their generating functions and functional equations. By using these functions, some properties and applications of these polynomials are investigated. Many relations and computation formulas connected with the Stirling type numbers, the Apostol type polynomials and numbers of order ?r, the Bernoulli polynomials of order ?r, the Euler polynomials and numbers of order ?r, the Fubini type numbers and polynomials of order ?r and combinatorial numbers are given. Applying the derivative operator to the generating functions of these polynomials, some formulas and combinatorial sums including these numbers and polynomials are also given. Moreover, applying the Riemann integral to some formulas, we derive several interesting finite combinatorial sums associated with the Bernstein basis functions, the Cauchy numbers and the Stirling type numbers. © 2023, MTJPAM Turkey. All rights reserved.
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    Formulas for special numbers and polynomials derived from functional equations of their generating functions
    (Tubitak Scientific & Technological Research Council Turkey, 2022) Kilar, Neslihan
    The main purpose of this paper is to investigate various formulas, identities and relations involving Apostol type numbers and parametric type polynomials. By using generating functions and their functional equations, we give many relations among the certain family of combinatorial numbers, the Vieta polynomials, the two-parametric types of the Apostol-Euler polynomials, the Apostol-Bernoulli polynomials, the Apostol-Genocchi polynomials, the Fibonacci and Lucas numbers, the Chebyshev polynomials, and other special numbers and polynomials. Moreover, we give some formulas related to trigonometric functions, special numbers and special polynomials. Finally, some remarks and observations on the results of this paper are given.
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    Generating Functions for the Fubini Type Polynomials and Their Applications
    (Springer, 2023) Simsek, Yilmaz; Kilar, Neslihan
    One of the aims of this chapter is to give Fubini type numbers and polynomials discovered with the help of generating functions or defined by combinatorial methods and also their general properties with known methods or techniques that we have found. The second purpose of this chapter is to give formulas and relations that we have just found, besides the known ones, using generating functions and their functional equations. The third purpose of this chapter is to give the relations between Fubini-type numbers and polynomials and other special numbers and polynomials. The fourth of the purposes of this chapter will be to give tables with Fubini-type numbers and polynomials, as well as other special numbers and special polynomials. In addition, by using Wolfram Mathematica version 12.0, graphs of Fubini type polynomials and their generating functions, surface graphs and mathematical codes will be given. The fifth purpose of this chapter, some known applications in the theory of approximation with Fubini-type numbers and polynomials are summarized. The sixth of the purposes of this chapter is to give zeta-type functions that interpolate Fubini-type numbers and polynomials at negative integers. Moreover, throughout this chapter, we are tried diligently to present the results obtained in comparison with other known results and their reductions, taking into account the relevant sources. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
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    Notes on Fubini Type Numbers and Their Properties
    (Amer Inst Physics, 2024) Kilar, Neslihan
    The study aims to expose new formulae for Fubini type polynomials and numbers. By putting into practice the generating function methods, we examine some properties of these polynomials and numbers. Making use of these functions, we obtain some formulae consisting of the Fubini type, generalized Euler-Frobenius type, and combinatorial numbers and polynomials.
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    Recurrence relations, associated formulas, and combinatorial sums for some parametrically generalized polynomials arising from an analysis of the Laplace transform and generating functions
    (Springer, 2023) Kilar, Neslihan; Simsek, Yilmaz; Srivastava, H. M.
    The aim of this paper is to obtain some interesting infinite series representations for the Apostol-type parametrically generalized polynomials with the aid of the Laplace transform and generating functions. In particular, by using the method of generating functions, we derive not only recurrence relations, but also several other formulas, identities, and relations as well as combinatorial sums for these parametrically generalized numbers and polynomials and for other known special numbers and polynomials. These identities, relations and combinatorial sums are related to the two-parameter types of the Apostol-Bernoulli polynomials of higher order, the two-parameter types of Apostol-Euler polynomials of higher order, the two-parameter types of Apostol-Genocchi polynomials of higher order, the Apostol-Bernoulli polynomials of higher order, the Apostol-Euler polynomials of higher order, the Apostol-Genocchi polynomials of higher order, the cosine- and sine-Bernoulli polynomials, the cosine- and sine-Euler polynomials, the lambda-array-type polynomials, the lambda-Stirling numbers, the polynomials C-n(x,y)Cn(x,y), and the polynomials S-n(x,y)Sn(x,y). Finally, we present several new recurrence relations for these special polynomials and numbers.
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    Remarks on Combinatorial Numbers Containing Special Numbers and Polynomials
    (Amer Inst Physics, 2024) Kilar, Neslihan
    The most important aim of this paper is to study some special cases of the open problem for ordinary generating functions (OGFs) for the combinatorial Simsek numbers of the sixth kind given by Simsek in [12]. The other aim is to give some identities and relations, including these numbers and others, via these generating functions. Finally, we present some applications of some special values of these results.
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    REMARKS ON COMBINATORIAL SUMS ASSOCIATED WITH SPECIAL NUMBERS AND POLYNOMIALS WITH THEIR GENERATING FUNCTIONS
    (Bayram Sahin, 2022) Kilar, Neslihan; Şimşek, Yilmaz
    The purpose of this article is to give some novel identities and inequalities associated with combinatorial sums involving special numbers and polynomials. In particular, by using the method of generating functions and their functional equations, we derive not only some inequalities, but also many formulas, identities, and relations for the parametrically generalized polynomials, special numbers and special polynomials. Our identities, relations, inequalities and combinatorial sums are related to the Bernoulli numbers and polynomials of negative order, the Euler numbers and polynomials of negative order, the Stirling numbers, the Daehee numbers, the Changhee numbers, the Bernoulli polynomials, the Euler polyno-mials, the parametrically generalized polynomials, and other well-known special numbers and polynomials. Moreover, using Mathematica with the help of the Wolfram programming language, we illustrate some plots of the parametrically generalized polynomials under some of their randomly selected special conditions. Finally, we give some remarks and observa-tions on our results. © 2022, Bayram Sahin. All rights reserved.